Title: Colmez' conjecture in average
Speaker: Shouwu Zhang (Princeton Univ.)
Time: 2015-5-20, 16:30-17:30
Place: 110
Abstract: This is a report on a joint work with Xinyi Yuan on a conjectured formula of Colmez about the Faltings heights of CM abelian varieties. I will sketch a deduction of this formula in average of CM types from our early work on Gross—Zagier formula. When combined with a recent work of Tsimerman, this result implies the Andre—Oort conjecture for the moduli of abelian varieties. Our method is different than a recently announced proof of a weaker form of the average formula by Andreatta, Howard, Goren, and Madapusi Pera: we use neither high dimensional Shimura varieties nor Borcherds' liftings.
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